Copolyesters containing 1,4-cyclohexanedimethanol (abbreviated hereinafter as “CHDM”) as a diol component are often produced using a dialkyl esters such as, for example, dimethyl terephthalate (DMT), dimethyl isophthalate, and 1,4-dimethylcyclohexane dicarboxylate, as the source of the diacid component. In a typical process, for example, a dialkyl ester is reacted with one or more diols in a transesterification reaction to produce an oligomer. The alkyl alcohol by-product is removed from the reaction medium, usually by distillation, to help to push the reaction equilibrium toward oligomer formation. Typical ester exchange process temperatures for these copolyesters range from 180° C. to about 270° C. at absolute pressures between about 45 to about 550 kPa. The transesterification step is followed by a polymerization step where excess diol is removed and the oligomer converted further in a polycondensation reaction to yield a high molecular weight copolyester. Copolyesters produced from dimethyl terephthalate (abbreviated herein as “DMT”), 2,2,4,4-tetramethyl-1,3-cyclobutanediol (abbreviated herein as “TMCD”), and 1,4-cyclohexanedimethanol (abbreviated herein as “CHDM”) in either a batch or continuous process are known to be prone to premature formation of poly(1,4-cyclohexylene dimethylene) terephthalate (abbreviated herein as “PCT”), resulting in precipitation of low molecular weight PCT species. PCT precipitation can terminate the preparation of the polyester before the targeted molecular weight or desired composition is obtained. In addition, the PCT can foul process equipment. PCT is known to have a melt temperature (Tm) of about 290° C.; process temperatures of 290° C. and greater, therefore, generally will melt the low molecular weight PCT precipitant and return it to the reaction mixture. Process temperatures greater than about 270° C., however, can accelerate the thermal degradation of raw materials and intermediate species, produce color, and lower the molecular weight of the polymer. Thermal degradation is particularly troublesome when thermally sensitive diols such as, for example, TMCD, are present in the copolyester reaction mixture. Therefore, attempting higher process temperatures in order to avoid premature PCT precipitation is undesirable. These problems have created a need for an alternative copolyester process that avoids PCT precipitation when terephthalate esters are used as starting materials in combination with diol components comprising CHDM and TMCD.